That is, H is the hidden layer output matrix of the network; the \(i\) th column of H indicates the \(i\) th hidden node's output vector with respect to \(\textbf {x}_{1}, \dots , \textbf {x}_{N}\) , and the \(j\) th row of H represents the output vector of the hidden layer with respect to input \(\textbf {x}_{j}\) . Because the learning problem is equivalent to a linear regression of the output \((\textbf {Y})\)  on the transformed versions of the inputs (embedded in \(\textbf {H}\) ), the output weights \(\beta \)  can be estimated as \(\beta ^{*} = \textbf {H}^{\dagger }\textbf {Y}\) 
where \(\textbf {H}^{\dagger }\)  is the Moore–Penrose generalized inverse [1]}, [2]} of the hidden layer output matrix \(\textbf {H}\) . As we discuss herein, our model is loosely connected to a specific configuration of NNRWs and exploits the learning process of training the output weights \(\beta \) .
